--- name: advances-in-mathematics description: Use when targeting Advances in Mathematics (Adv. Math.) or deciding whether a pure mathematics manuscript fits this broad-scope Elsevier research venue. Encodes the journal's fit, framing, proof standard, house style, official-submission re-check, and desk-reject heuristics. --- # Advances in Mathematics (advances-in-mathematics) ## Journal positioning Advances in Mathematics, published by Elsevier, is a leading general journal of pure mathematics that publishes high-quality original research across all major areas. Its defining character is breadth at a high standard: it is not restricted to a single field and welcomes strong results from algebra, geometry, topology, number theory, analysis, combinatorics, and beyond, provided the work is significant and of interest beyond a narrow sub-community. Advances sits just below the very top general journals in selectivity — excellent, substantial research that may not reach the field-reshaping bar of Annals is well placed here. The journal rewards new theorems, new structures, and new methods presented with clarity and full rigor. This skill is a **fit / venue-selection / re-framing** tool. It does not replace the journal's current official submission guidelines. Before submitting, re-check the live author instructions on the Advances in Mathematics Elsevier site and confirm submission procedures. ## When to trigger - The author is considering Advances in Mathematics for a strong, general-interest pure-mathematics paper. - A result is excellent and of broad interest but the author is unsure whether it reaches `inventiones-mathematicae` or `journal-of-the-american-mathematical-society` level. - A paper spans or bridges sub-fields and the author wants a high-standard generalist venue rather than a specialized one. - The author needs Advances' significance and rigor bar, plus common rejection reasons, before submission. ## Scope & topic fit - Pure mathematics across all major areas: algebra, representation theory, algebraic and differential geometry, topology, number theory, analysis, probability, combinatorics, logic, category theory. - New theorems of substantial interest, new mathematical structures or invariants, and new methods with potential to influence work beyond the immediate problem. - Results that bridge sub-fields or import techniques from one area into another are well suited to a generalist venue. - Strong, complete advances that are significant but perhaps more specialized than the very top general journals require. - Survey or purely expository work is generally not the focus; contributions must be primary research with new, fully proved results. ## Method & evidence bar - The primary standard is mathematical correctness: every claim must be fully proved; no proof sketches, unresolved cases, or conditional results in place of complete arguments (unless conditionality is the explicit contribution). - Significance is judged on interest and substance to a broad mathematical readership, not on citation counts or problem fame alone. - Novelty matters: new technique or genuinely new results are expected; routine extensions of known arguments are unlikely to clear the bar. - Exposition must let expert referees verify correctness: precise statements, complete proofs, and clear separation of new from standard material. - MSC (Mathematics Subject Classification) codes must be assigned correctly to signal scope and assist referee assignment. - arXiv posting is standard practice; most submissions appear on arXiv before or contemporaneously with submission. ## Structure & house style - No imposed structural template beyond mathematical convention: introduction (context, precise statement of results, proof strategy), preliminaries, core proof sections, optional appendices. - The introduction should state main results precisely, explain significance to a broad mathematical audience, and outline key ideas — generalist referees and a broad editorial board read it first. - LaTeX is standard; Elsevier formatting conventions apply — re-check the current style requirements and reference style on the submission site. - References must be complete and correctly formatted; preprint citations should carry stable arXiv identifiers. - Length is set by mathematical necessity; there is no fixed page limit, but unnecessary length attracts scrutiny — concise, complete arguments are valued. ## Official-submission checklist - Before giving submission-ready advice, read `../../resources/source-basis.md` and `../../resources/official-source-map.md`; start from the official source anchors for this journal family, then cite the current journal-specific page you checked. - Check the current Advances in Mathematics submission instructions on the Elsevier site and re-verify the submission system and procedure. - Assign MSC primary and secondary classification codes. - Post to arXiv (or confirm prior posting) with the identifier ready for correspondence. - Prepare a cover letter stating the main result, its significance to a broad readership, and suggested/excluded referees with conflicts noted. - Confirm all co-authors have approved the submission and re-check current open-access/APC options under Elsevier. - If the live official instructions conflict with this skill, the official instructions win. ## Pre-submission self-check - [ ] One sentence stating the main theorem and why it is of broad mathematical interest. - [ ] Every claim is fully proved; no gaps, sketches, or unresolved cases. - [ ] The result is genuinely new and substantial, not a routine extension of known arguments. - [ ] The introduction states results precisely, explains significance, and outlines proof ideas for a generalist audience. - [ ] The paper is posted or ready to post on arXiv with correct MSC codes. - [ ] An honest assessment: is this best at Advances, or does its significance warrant a try at `inventiones-mathematicae` or `journal-of-the-american-mathematical-society` first? ## Common desk-reject triggers - A correct but incremental result that extends known techniques without a substantially new idea. - A narrowly specialized paper of interest only to a small sub-community, better suited to a field journal. - An incomplete proof: any identifiable gap, unresolved case, or unjustified claim. - An introduction that fails to convey significance or broad interest to a generalist editorial board. - Expository or survey material submitted as primary research without new theorems. ## Re-routing decision Result of exceptional, field-reshaping significance → `annals-of-mathematics`. Top-tier general-interest advance just above the Advances bar → `inventiones-mathematicae` or `journal-of-the-american-mathematical-society`. Deep analysis / PDE / applied-analysis with substantial theorem content → `communications-on-pure-and-applied-mathematics`. Narrowly specialized result → a field-specific journal (Duke Mathematical Journal for broad-but-deep work, or area-specific society journals). ## Output format ```text [Fit] High / Medium / Low (one-line reason) [Target] Advances in Mathematics [Topic tags] <2–3 MSC areas> [Method/evidence] [Top risk] [Official items to re-check] [Re-route suggestion] ```